%I #27 Nov 23 2017 19:42:19

%S 1,1,2,3,3,4,5,5,6,7,7,7,8,9,9,9,10,10,12,13,13,13,15,15,15,15,16,16,

%T 16,16,18,18,18,20,20,20,20,20,20,20,20,22,22,22,22,22,25,25,25,25,25,

%U 27,27,27,28,28,28,30,30,30,30,32,32,32,32,33,33,33,35,35,35,35,36,36,36,36,40,40,40,42

%N a(n) = (1/2) * smallest even number missing from [A280864(1), ..., A280864(n-1)].

%C For k>=1, n>=1, let B_k(n) = smallest multiple of k missing from [A280864(1), ..., A280864(n-1)]. Sequence gives values of B_2(n)/2.

%C The analogous sequences B_k(n) for the EKG sequence A064413 were important for the analysis of that sequence, so they may also be useful for studying A280864.

%H Rémy Sigrist, <a href="/A284724/b284724.txt">Table of n, a(n) for n = 1..10000</a>

%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0204011">The EKG sequence</a>, arXiv:math/0204011 [math.NT], 2002.

%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.3/Lagarias437_446.pdf">The EKG Sequence</a>, Exper. Math. 11 (2002), 437-446.

%e The initial terms of A280864 are 1,2,4,3,6,8,... The smallest missing even number from [1,2,4,3,6] is 8, so a(6) = 8/2 = 4.

%p mex := proc(L)

%p local k;

%p for k from 1 do

%p if not k in L then

%p return k;

%p end if;

%p end do:

%p end proc:

%p read b280864;

%p k:=2; a:=[1,1]; ML:=[]; B:=1;

%p for n from 2 to 120 do

%p t:=b280864[n];

%p if (t mod k) = 0 then

%p ML:=[op(ML),t/k];

%p B:=mex(ML);

%p a:=[op(a),B];

%p else

%p a:=[op(a),B];

%p fi;

%p od:

%p a;

%t terms = 80; rad[n_] := Times @@ FactorInteger[n][[All, 1]];

%t A280864 = Reap[present = 0; p = 1; pp = 1; Do[forbidden = GCD[p, pp]; mandatory = p/forbidden; a = mandatory; While[BitGet[present, a] > 0 || GCD[forbidden, a] > 1, a += mandatory]; Sow[a]; present += 2^a; pp = p; p = rad[a], terms]][[2, 1]];

%t Clear[a];

%t a[1] = 1;

%t a[n_] := a[n] = For[b = 2a[n-1], True, b += 2, If[FreeQ[A280864[[1 ;; n-1]], b], Return[b/2]]];

%t Array[a, terms] (* _Jean-François Alcover_, Nov 23 2017, after _Rémy Sigrist_ program for A280864 *)

%Y Cf. A280864, A064413, A284725, A284726.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Apr 06 2017